Ordinal notations based on a hierarchy of inaccessible cardinals (Q1109768)

The author generalizes results on notation systems of \textit{K. Schütte} [Proof theory (1977; Zbl 0367.02012)] and \textit{W. Buchholz} [Lect. Notes Math. 500, 4-25 (1975; Zbl 0342.02021)], and obtains, via so-called Skolem hulls and 2-place functions from the ordinals into the inaccessible cardinals, a new ordinal notation system. This research was motivated by the fact that \((\Delta^ 1_ 2-CA)+BI\) has a model at the first recursively inaccessible ordinal in the constructible hierarchy.